One of the problems: the teaching order of textbooks.
At present, the teaching order in our province is compulsory 1, 2,3,4,5, and then elective 2- 1, 2-2,2-3, etc. In the specific implementation process, we feel that this teaching sequence is not appropriate enough, and there are some problems in some content arrangements:
(1) Algebra and geometry are out of sync. The new curriculum reform has made great adjustments to high school mathematics textbooks: a lot has been deleted, but more has been added, and the order of some contents has been adjusted. For example, the "oblique triangle" used in algebra in junior high school was moved to compulsory 5 in senior high school. However, the textbook writers neglected a problem: the contents of algebra and geometry are not synchronized. For example, students will learn Sine Theorem and Cosine Theorem for the first time in the first semester of Senior Two, and as the application of Cosine Theorem in mathematics, the problem of finding distance or angle can only be solved on a special right triangle line. In addition, trigonometric functions are put into compulsory 4, while the second chapter of compulsory 3, lines and equations, needs inductive formulas. Therefore, the author thinks that putting the content of "deflection triangle" behind "trigonometric function" and moving it to the front of the knowledge points of compulsory 3 is more conducive to teaching.
(2) The time sequence of learning solid geometry and analytic geometry is improper. It has become people's mindset that senior one students learn solid geometry and senior two students learn analytic geometry. However, according to the survey of teachers and students in senior high schools and years of teaching practice, the author thinks that learning analytic geometry in senior one and solid geometry in senior two are more conducive to teaching. The reason is that the algebra of senior one is set and function from the beginning, and a major feature of analytic geometry is the combination of numbers and shapes, that is, the study of geometric problems in the coordinate system (plane analytic geometry mainly studies the properties of lines and curves in the plane coordinate system). Obviously, the combination of function content and analytic geometry knowledge can be found faster, which is beneficial to teaching and students' understanding and mastery of knowledge. A major feature of solid geometry is its strong sense of space and high demand for abstract thinking. However, freshmen in senior high school are weak in this respect. The study of solid geometry by senior one students has dampened their enthusiasm for learning from the beginning, which makes many students feel bored with mathematics.
(c) The knowledge block is not systematic and coherent. The new textbook should not only reflect the gradual progress, but also reflect the spiral rise, which will make people feel that the knowledge system is incomplete, and the knowledge points before and after are not connected and out of touch. Some knowledge, learned a little before, but later learned a little higher, the former is forgotten and appears fragmented, which is not conducive to students' systematic mastery of knowledge. The new curriculum standard requires students to master mathematics knowledge in a spiral process, which disrupts all the knowledge plates. The author thinks this starting point is good, but it is idealized. In actual teaching, many teachers find that when they want to learn the second half of the knowledge section, students have forgotten the previous related knowledge. For example, at the beginning of the second semester of senior one, students have just formed a little relevant knowledge system, but the course is over. It was not until the second semester of senior two that statistical cases were involved. At this time, students had forgotten all about the original knowledge and had to review it again.
In short, it is difficult for students to form a systematic knowledge system according to this teaching order. Senior three always reviews, and the review of a lot of knowledge is like a new lesson. Therefore, the author suggests that the teaching order of textbooks should be compulsory 1, 4, 5, 2, 3, and then elective 2-3, 2- 1, 2-2. In this way, the previous problem is solved.
The second problem: there is a serious shortage of class hours.
"More content, less class hours" is the strongest problem reflected by teachers. In the teaching of new mathematics curriculum, teachers generally feel heavy burden and lack of teaching time. According to the class arrangement of "Guiding Opinions on the New Curriculum in Ordinary Senior High Schools", a module needs 36 class hours, which makes students feel very hard. The capacity of each class is particularly large, and the content of each class is new. Review, consolidation and improvement depend on your own efforts after class. In the face of the new curriculum, we have to keep catching up with classes. How can we have time to comment on exercises and conduct unit tests? How can we know the students' learning level without feedback test? Take the course of senior one as an example. The content of the study is related to the compulsory course 1 Function, which consists of three chapters and 36 class hours, and should be completed before the mid-term exam of senior one. Regardless of whether these contents can be completed in 36 class hours. Even if the class is arranged according to the teaching reference book, it will not delay a class. It takes 9 weeks to complete 4 class hours a week. The exam in the first half of the semester is *** 1 1 week. The first week is only one day, the National Day holiday is one week, and various school activities (such as sports meeting, examination room arrangement, etc. ) also washed away some classes. In this way, you can barely finish the class at most, not to mention the unit test and review before the exam. Moreover, the new textbook contains a lot of content. Although it may be less difficult than the old textbook, it is far more extensive than the old textbook. Compared with the past, the teaching content has increased a lot, and the classroom capacity of each class is very large. After a week or five, I still feel pressed for time. Therefore, a lot of content can only be "touched" and the requirements are not high. As long as you can master the content of the textbook, it is good for students.
The third question: the difficulty of new content.
In order to meet the needs of the development of the information age, the compulsory course of senior high school mathematics has added the content of algorithm, taking the most basic knowledge of data processing and statistics as the new basic knowledge and skills of mathematics, and added the concept of zero, dichotomy, power function, three views, preliminary algorithm, reasoning and proof, statistical cases, stem-leaf diagram, geometric probability and so on. But the large-capacity and high-intensity classroom teaching and practice make students "breathless", so how to grasp the difficulty of new content? For example, compulsory 3 mainly increases algorithm and geometric probability, while elective 2-3 mainly increases conditional probability and statistical cases. In the teaching process of these contents, it is difficult to grasp the difficulties. In the teaching process of the chapter "Algorithm", many teachers feel that they are struggling, especially the older teachers, who always feel that students know more than themselves. For example, in the chapter "Testing the independence of regression analysis", the most common sigh of teachers is: "I have read it three or four times, but I still don't know how to say it. Finally, how many classes should we divide into and where should we assign them? "
Question 4: Use of information technology tools.
Calculator has been listed as an elective course in junior high school mathematics, paving the way for senior high school to use calculator to deal with complex calculation problems. The new curriculum standard and new teaching materials advocate the use of scientific calculators, computer software and various mathematical education technology platforms as much as possible. It is hoped that students can learn relevant mathematics content with the help of information technology, and explore and study some meaningful and valuable mathematics problems. Information technology can greatly reduce the workload in mathematics learning, especially in solving some complicated problems of calculation and combination of numbers and shapes, or exploring some open and challenging problems, which can make the results more accurate and intuitive. Many middle schools do not have these conditions, or the conditions are poor, so it is impossible for students to operate on the computer; Many families don't have computers, and many students don't know if they have programming, so they can't operate on computers at all. Some psychologists believe that using a calculator is also a learning process, but if it is used for a long time, it may affect children's practical ability and brain skills. Oral calculation and written calculation are part of the cultivation of mathematical ability, but relying on calculators, students lack the confidence to solve difficulties actively. Calculators are not allowed to be used in the college entrance examination now, but the new curriculum standard repeatedly emphasizes the use of calculators and computers. What do we do? Because there are some problems with or without large errors, such as the coefficients of regression equations, and some examples (such as the application of functions and mathematical modeling) use dichotomy to find approximate solutions of equations, hoping to get unified requirements. Calculators are not allowed to be used in the college entrance examination, which makes students lack the motivation to learn these contents, let alone interest.
In short, the reform of mathematics textbooks is not a one-off event. Teaching material experiment will inevitably encounter some difficulties and problems, which need teachers to work together to solve. The author puts forward the above four questions on the current high school mathematics textbooks. Whether these problems are correct or not needs further research and experiments by experts. The purpose of writing this paper is to attract more experts and scholars to pay attention to the construction of teaching materials and make the new curriculum reform in our province a complete success.